The equation for the function after the transformation is f'(x) = 2x^2 - 3
How to write the image for the function?The initial equation is given as
f(x) = x²
The above represents the parent function
The sequence of transformations is given as
Vertically stretched by a factor of 2Shifted a distance of 3 units downThe rules of the above sequence of transformations are
Vertically stretched by a factor of 2: (x, 2y)Shifted a distance of 3 units down: (x, y - 3)When the rules are applied, we have
Stretch: f(x) = 2x^2Shifted: f'(x) = 2x^2 - 3Hence, the equation in its final position is f'(x) = 2x^2 - 3
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What’s the correct answer? I need help now
For triangle ABC, a = 7.7 , b = 17.0 , c = 12.7. Find m∠C.
The triangle can be drawn as shown below:
The Cosine Rule can be applied in this case. It is given to be:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ \cos C=\frac{a^2+b^2-c^2}{2ab} \end{gathered}[/tex]From the question, we have the following measures:
[tex]\begin{gathered} a=7.7 \\ b=17.0 \\ c=12.7 \end{gathered}[/tex]Therefore, we can substitute and solve as shown below:
[tex]\begin{gathered} \cos C=\frac{7.7^2+17.0^2-12.7^2}{2\times7.7\times17.0} \\ \cos C=\frac{187}{261.8} \\ \cos C=0.714 \end{gathered}[/tex]Therefore, the measure of angle C will be gotten to be:
[tex]\begin{gathered} C=\cos ^{-1}0.714 \\ m\angle C=44.4\degree \end{gathered}[/tex]The measure of angle C is 44.4°.
can you help me answer this please?This is condense each expression to a sinhle logarithm
ANSWER
[tex]\log_3x^{\frac{1}{3}}[/tex]EXPLANATION
Given;
[tex]\frac{\log _3x}{3}[/tex]Rewrite as;
[tex]\frac{1}{3}\log_3x[/tex]Simplify by moving 1/3 inside the logarithm;
[tex]\begin{gathered} \log_3x^{\frac{1}{3}} \\ \end{gathered}[/tex]Solve the following problem. Give the equation using x as the variable, and give the answer.If 4 is added to five times a number, the result is equal to 7 more than four times the number. Find thenumber.Write the equation using x as the variable. Choose the correct equation below.O A. 4(5x) = 7(4x)O B. 5(x + 4) = 4(x + 7)O C. 5x + 4 = 7(4x)OD. 5x + 4 = 4x + 7O E. 4(5x) = 4x + 7The number is
Answer
[tex]\begin{gathered} D. \\ 5x+4=4x+7 \\ \text{The number is 3} \end{gathered}[/tex]Explanation
The variable given is x
Five times the variable is 5x
When 4 is added, the expression becomes 5x + 4, which gives the Left Hand Side of the equation.
For the Right Hand Side, four times the number is 4x
7 more than 4x is 4x + 7
Since the result on the Left Hand Side = Right Hand Side, then the required equation is
[tex]5x+4=4x+7[/tex]Now, to find the number x, we shall solve the above equation as follows
[tex]\begin{gathered} 5x+4=4x+7 \\ \text{Substract 4 from both sides} \\ 5x+4-4=4x+7-4 \\ 5x=4x+3 \\ \text{Substract 4x from both sides} \\ 5x-4x=4x+3-4x \\ x=3 \end{gathered}[/tex]It takes Anastasia 45 minutes to walk 2.5 miles to the park. At this rate, how
many minutes should it take her to walk 3 miles?
Suppose you invest $5,000 at 4% annual interest. How much money would your investment be worth after 10 years? Round your answer to the nearest hundredth (2 places after the decimal).
The investment will be worth $7,401.22 after 10 years
Here, we want to calculate the amount the investment will be worth after 10 years
Mathematically, to get this, we will use the compound interest formula;
[tex]A\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]where A is the amount after 10 years
P is the amount invested which is $5,000
r is the interest rate which is 4%, same as 4/100 = 0.04
n is the number of terms yearly the investment will be compounded. Since the interest rate is annual, then the number of times it will be compounded yearly is 1
t is the number of years which is 10 in this case
Substituting these values, we have;
[tex]\begin{gathered} A\text{ =5000 (1 + }\frac{0.04}{1})^{1\times10} \\ \\ A=5000(1+0.04)^{10} \\ \\ A=5000(1.04)^{10} \\ \\ A\text{ = 7,401.22} \end{gathered}[/tex]Find m
Which answer is correct
The value of angle EFG is 50°.
What is angle?An angle results from the intersection of two straight lines or rays at a single terminal.
Angles' Components
Vertex: The intersection of two lines or sides at an angle is called a vertex.
Arms: The angle's two sides linked at a single end.
Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line.
∵ exterior angle = sum of opposite interior angles
∴ 7x+18 = (6x-10) + 38
7x + 18 = 6x +28
x = 10°
∴∠EFG = 6*10-10
∠EFG = 50°
Option (B) is correct answer.
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what is math all about.
Mathematics is a branch of science that deals with numbers, quantities and shapes. It includes arithmetic, geometric, algebra, calculus and many more. It also refers to the study of relationship between numbers or items.
One example is counting numbers which we are using almost everyday in our life.
1, 2, 3, 4 and so on.
to put it in graphing form and then graphY=x^2-6x+3
We have the following:
[tex]\begin{gathered} y=x^2-6x+3 \\ f(x)=x^2-6x+3 \end{gathered}[/tex]now, we must give values to x, to be able to graph
[tex]\begin{gathered} f(-2)=x^2-6x+3=(-2)^2-6\cdot-2+3=19 \\ f(-1)=x^2-6x+3=(-1)^2-6\cdot-1+3=10 \\ f(0)=x^2-6x+3=(0)^2-6\cdot0+3=3 \\ f(1)=x^2-6x+3=(1)^2-6\cdot1+3=-2 \\ f(2)=x^2-6x+3=(2)^2-6\cdot2+3=-5 \end{gathered}[/tex]The grahp is:
Find the quotient of 24 and 3.
Please help
Answer
8
Step-by-step explanation
we know that the term quotient means that we divided so we think backward if 24 is being divided by 3 what times 3 equals 24 the answer would be 8 because 3x8=24.
When Levi deposited $40 into his savings account, his bank statement showed the transaction as $40.
If the next transaction on his statement shows
–
$30, which of these describes the transaction?
The next transaction statement can be described through option A) Thirty dollars was withdrawn if the next transaction on his statement shows –$30.
What is a Transaction statement?The term "Transaction Statement" refers to a statement that the lender may from time-to-time issue to any borrower, at the borrower's reasonable request or at the lender's option, listing the loans made, the inventory and accounts receivable they financed, as well as the terms and conditions of repayment.
A transaction can be said as a unit of work that is thus performed against a database. These transactions are units or mostly sequences of work that are accomplished in a logical order.
You can find your most recent statement via your bank branch because most banks allow you to generate statements through your online banking platform.
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Complete Question
When Levi deposited $40 into his savings account, his bank statement showed the transaction as $40.
If the next transaction on his statement shows –$30, which of these describes the transaction?
A) Thirty dollars was withdrawn
B) Money was neither deposited nor withdrawn
C) $30 was deposited
D) Seventy dollars was deposited
(d) Find the domain of function R. Choose the correct domain below.
Answer:
last answer is right
( but x can be any number not just x>=0 )
Businesses deposit large sums of money into bank accounts. Imagine an account with $10 million dollars in it.
a. How much would the account earn in one vear of simple interest at a rate of
2.12067 Round to the nearest cent.
Elijah earned a score of 64 on Exam A that had a mean of 100 and a standarddeviation of 20. He is about to take Exam B that has a mean of 600 and a standarddeviation of 40. How well must Elijah score on Exam B in order to do equivalentlywell as he did on Exam A? Assume that scores on each exam are normally distributed.
Notation:
μ = mean
σ = standard deviation
Exam A:
[tex]\begin{gathered} \mu=100 \\ \sigma=20 \end{gathered}[/tex]The score of the exam is 64, so we calculate the z-score given that scores on the exam are normally distributed. The formula of the z-score is:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Now, for X = 64:
[tex]Z=\frac{64-100}{20}=-1.8[/tex]Exam B:
[tex]\begin{gathered} \mu=600 \\ \sigma=40 \end{gathered}[/tex]Now, we need to find a z-score equal to that of the score on Exam A. This z-score is -1.8, and the score on exam B should be:
[tex]\begin{gathered} -1.8=\frac{X-600}{40} \\ -72=X-600 \\ \therefore X=528 \end{gathered}[/tex]The score on exam B should be 528 in order to do equivalently well as he did on Exam A
“K+273 gives the temperature in kelvins(K) for a given temperature in degrees Celsius.What is the temperature in kelvins when the temperature is 55 degrees Celsius?” Evaluate the expression
we have that
The temperature T in degrees Celsius (°C) is equal to the temperature T in Kelvin (K) minus 273.15
so
°C=K-273.15
For T=55°C
substitute
55=k-273.15
solve for k
k=55+273.15
K=328.15°I just need to know what do I do when it says 2t but t is 10.M - t squared 2 / (M+p) + 2t
Solution:
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]m-t^2\div(m+p)+2t[/tex]STEP 2: Write the given values
[tex]t=10,m=3,p=2[/tex]STEP 3: Substitute the values and simplify
[tex]\begin{gathered} 3-(10^2)\div(3+2)+2(10) \\ Follow\:the\:PEMDAS\:order\:of\:operations \end{gathered}[/tex]We solve the bracket first:
[tex]=3-100\div5+20[/tex]We solve the division operator next:
[tex]\begin{gathered} 3-(100\div5)+20 \\ 3-20+20 \end{gathered}[/tex]We do the addition and subtraction simultaneously to have:
[tex]3+0=3[/tex]Hence, the result of the simplification gives 3
275 x 56 using long multiplication
Answer:
15400
Step-by-step explanation:
Hope it helps and I hope you have a nice day!!! :)
BRAINIEST is appreciated it would really help!!!
jk has midpoint M(–17, 16.5) and endpoint K(–12, 4). What are the coordinates of endpoint J?
The coordinates of endpoint J which has the midpoint M(–17, 16.5) and endpoint K(–12, 4) is (-22,29)
Mid point:
Midpoint means the point that is in the middle of the line joining two points.
Given two points A (x)1, (y)1 and B (x)2, (y)2, the midpoint between A and B is given by,
M(x)3, (y)3 = [(x)1 + (x)2]/2, [(y)1 + (y)2]/2
where, M is the midpoint between A and B, and (x)3, (y)3 are its coordinates.
Given,
JK has midpoint M(–17, 16.5) and endpoint K(–12, 4).
Here we need to find the coordinates of endpoint J.
We know that formula of mid point through the given definition,
So let us consider
(x1, y1) = (a, b)
(x2, y2) = (-12,4)
Now we have to apply the values on the formula in order to solve it,
Therefore,
(-17, 16.5) = (a + (-12))/2 , (b + 4)/2
Compare the values individually, then we get,
-17 = (a - 12) / 2
-17 x 2 = a - 12
- 34 = a - 12
a = -34 + 12
a = -22
Similarly, when we take the second part,
16.5 = (b+4)/2
16.5 x 2 = b + 4
33 = b+ 4
b = 33 - 4
b = 29
Therefore, the coordinate end points of J is (-22, 29).
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The formula A = P +Prt represents the relationshipbetween the principal, P, interest rate, r, and amount ofmoney, A, in an account over a period of time, t.Solve the equation for P.
Problem
The formula A = P +Prt
Solution
We can take common factor and we got:
A= P(1+rt)
And we can divide both sides by 1+rt and we got:
P = A /(1+rt)
Calculate the variance and standard deviation ofthe samples, using the appropriate symbols to label each
To determine the variance of a sample we can use the following formula:
[tex]s^2=\frac{\sum(x_i-\bar{x})}{n-1},[/tex]where
[tex]\bar{x}\text{ }[/tex]is the mean of the dataset.
The standard deviation is the square root of the variance.
Recall that the mean of a dataset is the sum of the number divided by the number of numbers, therefore, the mean of the given dataset is:
[tex]\bar{x\text{ }}=\frac{50.0+51.5+53.0+53.5+54.0}{5}=52.4.[/tex]Substituting the above result in the formula for the variance, we get:
[tex]s^2=2.675.[/tex]Therefore, the standard deviation is:
[tex]s=1.6355427.[/tex]Answer:
Variance:
[tex]s^2=2.675.[/tex]Standard deviation:
[tex]s=1.6355427.[/tex]Can you please show me how to check the answer to see if it is right.
We are given the equation;
[tex]-7=\sqrt[3]{9x-1}-3[/tex]Collect like terms
[tex]\begin{gathered} -4=\sqrt[3]{9x-1} \\ (-4)^3=(\sqrt[3]{9x-1})^3 \\ -64=9x-1 \\ -63=9x \\ x=-7 \end{gathered}[/tex]To check this, we insert the x value into the original equation, if it gives both sides equal, it is correct.
[tex]\begin{gathered} -7=\sqrt[3]{9x-1}-3 \\ -7=\sqrt[3]{9(-7)-1}-3 \\ -7=\sqrt[3]{-64}-3 \\ -7=-4-3 \\ -7=-7 \end{gathered}[/tex]Therefore, the answer is -7
A Native American tepee is a conical tent. Find the number of skins needed to cover a teepee 10 ft. in diameter and 12 ft. high. Each skin covers 15 sq. ft. (use = 3.14)
Since it is conical, we need to find the surface area of the top of the conical shape.
If we unfold the top part of the cone, we will have a section of a circle:
The circunference of this section is the same as the total circunference of the base of the cone, which we can get from its radius (half its diamtere):
[tex]C=2\pi r=2\pi\cdot\frac{D}{2}=2\pi\cdot\frac{10}{2}=10\pi[/tex]If we visualize the cone by the side, we see that it forms a isosceles triangle which the same height and the base euqal to the diameter:
So, we can calculate "R", the radius of the unfolded cone, using the Pythagora's Theorem:
[tex]\begin{gathered} R^2=h^2+(\frac{D}{2})^2 \\ R^2=12^2+5^2 \\ R^2=144+25 \\ R^2=169 \\ R=\sqrt[]{169} \\ R=13 \end{gathered}[/tex]The circunference of a section of a circle is the circunferece of the total circle times the fraction of the section represents of the total circle. Let's call ths fraction "f", this means that:
[tex]\begin{gathered} C_{total}=f\cdot C \\ C_{total}=2\pi R=2\pi\cdot13=26\pi \\ C=10\pi \\ f\cdot26\pi=10\pi \\ f=\frac{10\pi}{26\pi}=\frac{5}{13} \end{gathered}[/tex]The area will follow the same, the area of the section is the fraction "f" times the total area of the circle, so:
[tex]\begin{gathered} A_{total}=\pi R^2=\pi13^2=169\pi \\ A=f\cdot A_{total}=\frac{5}{13}\cdot169\pi=65\pi\approx65\cdot3.14=204.1 \end{gathered}[/tex]So, the surface area of the top of the cone is 204.1 ft². Since each skin covers 15 ft², we can calculate how many skins we need by dividing the total by the area of each skin:
[tex]\frac{204.1}{15}=13.60666\ldots[/tex]This means that we need 13.60666... skins, that is, 13 is not enough, we need one more, so we need a total of 14 skins.
On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?
the length of the shadow is 30m
Explanation:hypotenuse = 50m
height of tree = 40 m
To solve the question, we will use an illustration:
To get the length of the shadow, we will apply pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse = 50m, opposite = 40m
50² = 40² + shadow²
2500 = 1600 + shadow²
2500 - 1600 = shadow²
900 = shadow²
square root both sides:
[tex]\begin{gathered} \sqrt[]{900}\text{ = }\sqrt[]{shadow^2} \\ \text{shadow = 30 m} \end{gathered}[/tex]Hence, the length of the shadow is 30m
standard form and contain only positive exponents 21c^10d^3+56c^6d^2-7c^2d------------------------------------------- 7c^2d
To solve this problem it is necessary to simplify the expression.
Step 1. Write the equation as a sum of homogeneous fractions:
[tex]\frac{21c^{10}d^3+56c^6d^2-7c^2d}{7c^2d}=\frac{21c^{10}d^3}{7c^2d}+\frac{56c^6d^2}{7c^2d}-\frac{7c^2d}{7c^2d}[/tex]Step 2. Simplify the obtained expressions:
[tex]\begin{gathered} \frac{21c^{10}d^3}{7c^2d}=3c^8d^2 \\ \frac{56c^6d^2}{7c^2d}=8c^4d \\ \frac{7c^2d}{7c^2d}=1 \end{gathered}[/tex]Step 3. Rewrite the expression using the simplified terms:
[tex]3c^8d^2+8c^4d-1[/tex]I couldn’t fit all the answers on the screen but the fourth option is all positive numbers
Answer:
Alternative C - All real numbers.
Step-by-step explanation:
The domain of an function is the set of all possible numbers which x can assume.
As we can see, we have no restrictions for x.
So, the domain is all real numbers.
Answer: Alternative C - all real numbers.
If you would like to make $1323 in 7 years, how much would you have to deposit in an account that pays simple interest of 2%?
A = $13,366.37
A = P + I where
P (principal) = $10,000.00
I (interest) = $3,366.37
What is the slope-intercept form(-2,-1),(-4,-3)
To solve the exercise, we can first find the slope of the line that passes through the given points using the following formula:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} (x_1,y_1)=(-2,-1) \\ (x_2,y_2)=(-4,-3) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-3-(-1)}{-4-(-2)} \\ m=\frac{-3+1}{-4+2} \\ m=\frac{-2}{-2} \\ m=1 \end{gathered}[/tex]Now, we can use the point-slope formula, and we solve for y:
[tex]y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula}[/tex][tex]\begin{gathered} y-(-1)=1(x-(-2)) \\ y+1=x+2 \\ \text{ Subtract 1 from both sides of the equation} \\ y+1-1=x+2-1 \\ y=x+1 \end{gathered}[/tex]Therefore, the equation of the line that passes through the points (-2, -1) and (-4, -3) in its slope-intercept form is:
[tex]$$\boldsymbol{y=x+1}$$[/tex]solve the equation for x
6x + 8 = 50
Answer:
x=7Step-by-step explanation:
To solve the equation for x, isolate it on one side of the equation.
6x+8=50Subtract by 8 from both sides.
6x+8-8=50-8
Solve.
50-8=42
6x=42
Divide by 6 from both sides.
6x/6=42/6
Solve.
Divide.
42/6=7
[tex]\Rightarrow \boxed{\sf{x=7}}[/tex]
Therefore, the solution is x=7, which is the correct answer.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6x + 8 = 50}[/tex]
[tex]\large\text{SUBTRACT \boxed{\textsf 8} to BOTH SIDES}[/tex]
[tex]\mathsf{6x + 8 - 8 = 50 - 8}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{8 - 8}} because it gives you 0}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{50 - 8}} because it help solve for the x-value}[/tex]
[tex]\mathsf{6x = 50 - 8}[/tex]
[tex]\large\text{New equation: } \mathsf{6x = 42}[/tex]
[tex]\large\text{DIVIDE \boxed{\mathsf{6}} to BOTH SIDES sides}[/tex]
[tex]\mathsf{\dfrac{6x}{6} = \dfrac{42}{6}}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{\dfrac{6}{6}}} because it gives you 1}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{\dfrac{42}{6}}} because it gives you the x-value}[/tex]
[tex]\mathsf{x = \dfrac{42}{6}}[/tex]
[tex]\mathsf{x = 7}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
l need help with this please
Answer:
Step-by-step explanation:
y = 4 - 2x
Anyone know the question ?
The total commission earned by Paun is $14,000.
What is meant by the term commission?Full-service brokerages make the majority of their money by charging commissions on customer transactions.Commission-based advisors earn money by purchasing and selling a product on their clients' behalf.Commissions and fees differ in the financial services industry, where fees are a fixed amount for managing a customer's money.For the given question.
The total sales done by Paun is $50,000.
There is commission of 25% on first $2000.
There is commission of 30% on remaining that is 48,000.
The total commission will be 25% of $2,000 and 30% of 48,000.
25% of $2,000 = 25 × 2000/100
25% of $2,000 = $500
30% of 48,000 = 30 × 48,000/100
30% of 48,000 = $14,400
Total commission = $500 + $14,400 = $14,900.
Thus, the total commission earned by Paun is $14,000.
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